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A009628
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Expansion of e.g.f.: sinh(x)/(1+x).
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11
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0, 1, -2, 7, -28, 141, -846, 5923, -47384, 426457, -4264570, 46910271, -562923252, 7318002277, -102452031878, 1536780478171, -24588487650736, 418004290062513, -7524077221125234, 142957467201379447, -2859149344027588940, 60042136224579367741
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OFFSET
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0,3
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COMMENTS
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LINKS
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FORMULA
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Let u(1) = 1, u(n) = n*u(n-1) + n (mod 2); then for n>0, a(n) = (-1)^(n+1)*u(n). - Benoit Cloitre, Jan 12 2003
Unsigned sequence satisfies a(n) = n*a(n-1)+a(n-2)-(n-2)*a(n-3), with E.g.f. sinh(z)/(1-z). - Mario Catalani (mario.catalani(AT)unito.it), Feb 08 2003
a(n) = (-1)^(n+1) * n! * Sum_{k=1..floor((n+1)/2)} 1/(2*k-1)!.
a(n) = (-1)^n*(exp(-1)*Gamma(1+n,-1) - exp(1)*Gamma(1+n,1))/2. - Peter Luschny, Dec 18 2017
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MAPLE
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G(x):= sinh(x)/(1+x): f[0]:=G(x): for n from 1 to 21 do f[n]:=diff(f[n-1], x) od: x:=0: seq(f[n], n=0..20); # Zerinvary Lajos, Apr 03 2009
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MATHEMATICA
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a[n_] := (-1)^n (Exp[-1] Gamma[1 + n, -1] - Exp[1] Gamma[1 + n, 1])/2;
With[{nn=30}, CoefficientList[Series[Sinh[x]/(1+x), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Mar 19 2023 *)
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PROG
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(PARI) x='x+O('x^99); concat([0], Vec(serlaplace(sinh(x)/(1+x)))) \\ Altug Alkan, Dec 18 2017
(Ruby)
a = 0
(0..n).map{|i| a = -i * a + i % 2}
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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